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arXiv · 1502.05385

Tensor network renormalization yields the multi-scale entanglement renormalization ansatz

Glen Evenbly·Guifre Vidal
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Abstract

We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and G. Vidal, arXiv:1412.0732] to the Euclidean time evolution operator $e^{-\beta H}$ for infinite $\beta$. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature $\beta$, produces a MERA representation of a thermal Gibbs state. Our construction endows TNR with a renormalization group flow in the space of wave-functions and Hamiltonians (and not just in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

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Glen Evenbly, Guifre Vidal. 2015-02-18. Tensor network renormalization yields the multi-scale entanglement renormalization ansatz. https://doi.org/10.1103/physrevlett.115.200401

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